Home
Class 12
MATHS
Consider f(x)=(x^(2))/(2)-kx +1 such tha...

Consider `f(x)=(x^(2))/(2)`-kx +1` such that f(0) =0 and f(3)=15
The value of k is

A

`5/3`

B

`3/5`

C

`-5/3`

D

`-3/5`

Text Solution

Verified by Experts

The correct Answer is:
D
`f'(x)=(x^(2))/(2)-kx+1`
`f(0)=0 f(3)=15`
`f(x)=1/6x^(3)=15`
putting x =0 ltrbgt `f(x)=(x^(3))/(6)-(k)/(2)x^(2)+x`
`15=9/2-9/2k+3 rarr k =-5/3`
Promotional Banner

Topper's Solved these Questions

  • 3-D GEOMETRY

    NDA PREVIOUS YEARS|Exercise MCQ|147 Videos

  • BINOMIAL THEROREM, MATHEMATICAL INDUCTION

    NDA PREVIOUS YEARS|Exercise MQS|65 Videos

Similar Questions

Explore conceptually related problems

Consider f'(x)=(x^(2))/(2)-kx+1 such that f(0)=0 and f(3)=15 . f''(-(2)/(3)) is equal to

Consider f(x)=x^(2)-3x+a+(1)/(a),a in R-{0} such that f(3)>0 and f(2)<=0. If alpha and beta are the roots of equation f(x)=0 then the value of alpha^(2)+beta^(2) is equlal to

Let f:W rarr W be a given function satisfying f(x)=f(x-1)+f(x-2) for x<=2. If f(0)=0 and f(1)=1, ther find the value of f(2)+f(3)+f(4)+f(5)+f(6)

If f(x)=int(3x^(2)+1)/((x^(2)-1)^(3))dx and f(0)=0, then the value of (2)/(f(2))| is

If f(x)=int(5x^8+7x^6)/((x^2+1+2x^7)^2)dx, (xge0), f(0)=0 and f(1)=1/K , then the value of K is _______ .

If f'(x)=3x^(2)sin x-x cos x x!=0 f(0)=0 then the value of f((1)/(pi)) is

If f(x)=int_(x^(2))^(x^(3))ln tdt,(x>0) and f'((4)/(9))=f'(k) then values of k can be

If the p.d.f of a continuous random variable X is f(x)=kx^(2)(1-x), 0 lt x lt 1 = 0 otherwise Then the value of k is

If f'(x)=3x^(2)sin x-x cos x ,x!=0 f(0)=0 then the value of f((1)/(pi)) is

NDA PREVIOUS YEARS-APPLICATION OF DERIVATIVES -Example
  1. Consider the fucntion f(x)=((1)/(x))^(2x^2) , where xgt0. At what v...

    Text Solution

    |

  2. The maximum value of the function is

    Text Solution

    |

  3. Consider f(x)=(x^(2))/(2)-kx +1 such that f(0) =0 and f(3)=15 The va...

    Text Solution

    |

  4. f''(-2/3) is equal to

    Text Solution

    |

  5. Separate the intervals of monotonocity for the function f(x)=-2x^3-9x^...

    Text Solution

    |

  6. The function f(x) is a decreasing funciton in the interval

    Text Solution

    |

  7. Consider the function f(theta)=4(sin^(2) theta + cos^(4) theta) what...

    Text Solution

    |

  8. What is the minimum value of the function f(theta) ?

    Text Solution

    |

  9. Consider the following statements: 1 f(theta) =2 has no solution 2...

    Text Solution

    |

  10. Consider the equaiton k sinx + cos 2x=2k-7 If the equaiton possesses...

    Text Solution

    |

  11. If the equaiton posses soluiton then what is the maximum value of k ?

    Text Solution

    |

  12. Which one of the following statement is correct in respect of the func...

    Text Solution

    |

  13. The maximum value of sin(theta+pi/6)+cos(theta+pi/6) is attained at th...

    Text Solution

    |

  14. The length of the longest interval, in which the function 3sin x-4 sin...

    Text Solution

    |

  15. What is the maximum value of the function f(x)=4sin^(2)x+1?

    Text Solution

    |

  16. Let f(x)=x+(1)/(x) when x in (0,1) Then which one of the following is ...

    Text Solution

    |

  17. Consider the following statement : 1(dy)/(dx) at a point on the cur...

    Text Solution

    |

  18. Which one of the folloiwng is correct in respect of the function f(x)=...

    Text Solution

    |

  19. The maximum value of (In x)/(x) is

    Text Solution

    |

  20. Match List I with List II and select the correxct anseer using the cod...

    Text Solution

    |